Modern matrix completion problems often involve heterogeneous data whose rows simultaneously belong to many meta-categories, such as demographic and age groups in recommendation systems, or region and recording session labels in neural electrophysiological experiments. Standard low-rank estimators impose a single global latent geometry, which can recover average structure but may smooth away subgroup-specific variation, especially when observations are unevenly distributed across groups. We introduce Group-Aware Matrix Estimation (GAME), a convex estimator for overlapping subgroup-wise low-rank matrix estimation. GAME regularizes category-specific submatrices through overlapping nuclear-norm penalties, allowing related groups to borrow information while preserving local latent structure in a shared coordinate system. We provide finite-sample guarantees for both reconstruction error and subgroup-specific subspace recovery, showing how performance depends on sampling density, subgroup rank, and overlap structure. Experiments on synthetic, recommendation, ecological, and neuroscience datasets show that GAME is most beneficial in structured missingness regimes, where subgroup-aware regularization improves both reconstruction accuracy and latent subspace fidelity. Across these benchmarks, GAME is competitive or best among global low-rank, side-information, and modern imputation baselines, with the largest gains when subgroups exhibit distinct low-rank structure.

Concept bottleneck models~(CBM) aim to improve model interpretability by predicting human level ``concepts" in a bottleneck within a deep learning model architecture. However, how the predicted concepts are used in predicting the target still either remains black-box or is simplified to maintain interpretability at the cost of prediction performance. We propose to use Fast Interpretable Greedy Sum-Trees~(FIGS) to obtain Binary Distillation~(BD). This new method, called FIGS-BD, distills a binary-augmented concept-to-target portion of the CBM into an interpretable tree-based model, while mimicking the competitive prediction performance of the CBM teacher. FIGS-BD can be used in downstream tasks to explain and decompose CBM predictions into interpretable binary-concept-interaction attributions and guide adaptive test-time intervention. Across $4$ datasets, we demonstrate that adaptive test-time intervention identifies key concepts that significantly improve performance for realistic human-in-the-loop settings that allow for limited concept interventions.

While the grasping capability of robotic grippers has shown significant development, the ability to manipulate objects within the hand is still limited. One explanation for this limitation is the lack of controlled contact variation between the grasped object and the gripper. For instance, human hands have the ability to firmly grip object surfaces, as well as slide over object faces, an aspect that aids the enhanced manipulation of objects within the hand without losing contact. In this letter, we present a parametric, origami-inspired thin surface capable of transitioning between a high friction and a low friction state, suitable for implementation as an epidermis in robotic fingers. A numerical analysis of the proposed surface based on its design parameters, force analysis, and performance in in-hand manipulation tasks is presented. Through the development of a simple two-fingered two-degree-of-freedom gripper utilizing the proposed variable-friction surfaces with different parameters, we experimentally demonstrate the improved manipulation capabilities of the hand when compared to the same gripper without changeable friction. Results show that the pattern density and valley gap are the main parameters that effect the in-hand manipulation performance. The origami-inspired thin surface with a higher pattern density generated a smaller valley gap and smaller height change, producing a more stable improvement of the manipulation capabilities of the hand.